Download Lab 6: Thin Lenses

LAB 6
Thin Lenses
OBJECTIVES
1. Explore the difference between converging and diverging lenses and determine their
focal lengths.
2. Determine the focal length of a diverging lens using the Lensmaker’s equation.
3. Experimentally measure the image distance and confirm the thin lens equation.
4. Explore how the human eye creates images and the difference between
nearsightedness and farsightedness.
5. Analyze and measure the behavior of images formed by a two-lens system and a lensmirror system.
EQUIPMENT
Basic Optics Kit, Ray Box, converging and diverging lenses, concave mirror, optical
bench, and metric ruler, human eye model, telescope.
THEORY
Parallel rays of light passing through a thin converging lens cross at the focal point of the
lens. For a diverging lens, parallel rays of light appear to have originated from a focal
point on the same side of the lens as the incoming light. The focal length is measured
from the center of the lens to the focal point. The Lensmaker’s equation is used to
calculate the focal length of a lens based on the radii of curvature of its surfaces and the
index of refraction of the lens material:
1
f
1
=
( n − 1) 
 r1
−
1

r2 
where f is the focal length, n is the relative index of refraction of the lens material, and r1
and r2 are the radii of curvature of the lens surfaces. Another way to calculate the focal
length is used the image-object equation for a thin lens:
1 1 1
=
+
f
p i
For a two-lens system or a lens-mirror system, the image from the first lens becomes the
object for the second lens (or mirror). The magnification is equal to the multiplication of
the magnifications of the individual lenses (or the lens and mirror):
 −i1   −i2 


 p1   p2 
=
m m=
m 
1 2
PROCEDURE
Part 1: Refraction—Converging and Diverging Lenses
(a) Place the ray box on a white piece of paper. Using five white rays from the ray box,
shine the rays straight into the converging lens. Trace around the surface of the lens
and trace the incident and transmitted rays.
(b) The place where the five refracted rays cross is the focal point of the lens. Measure
the focal length from the center of the converging lens to the focal point.
(c) Block out the center 3 rays and mark the focal point for the outer two rays. Next,
block out the outer two rays and mark the focal point for the inner 3 rays. Are the two
focal points the same?
(d) Repeat steps (a) – (c) for the diverging lens.
Part 2: Lensmaker’s Equation
(a) Using the results of part 1(d) for the diverging lens, note the focal length. Call this f expt .
(b) To determine the radius of curvature of each surface, put the diverging lens back in
the path of the rays and observe the faint reflected rays off the first surface of the lens.
The front of the lens can be treated as a concave mirror having a focal length and a
radius of curvature. Trace the surface of the lens, and the incident and (faint) reflected
rays. Measure the distance from the center of the front curved surface to the point
when the faint reflected rays cross. From this distance, calculate the radius of
curvature r1 .
(c) Flip the diverging lens and repeat the above process to calculate the radius of
curvature r2 .
(d) Calculate the focal length fthy of the lens using the Lensmaker’s equation. The index
of refraction is 1.5 for the acrylic lens.
(e) Calculate the percent difference between the measured and the calculated values of
the focal length. How do they compare?
(f) Is the focal length of a diverging lens positive or negative?
Part 3: Converging Lens
(a) Mount a light source near one end of the optical bench and place a converging lens
with focal length f = 20 cm (200 mm) near the other end.
(b) Using the thin-lens and magnification equations, predict the object distance ( pthy ) and
images distance ( ithy ) necessary to produce a real image with a magnification m = 2 .
(c) Use a screen to find the image location iexpt and the magnification mexpt = −iexpt / pexpt .
Compare ithy and iexpt using a percent difference. How do they compare?
(d) Use ray tracing to draw an accurate scaled ray diagram of this optical system.
Part 4A: The Human Eye - Focusing an image on the retina
(a) Make sure the small plastic lens marked +400 is inside the eye. Put your hand about
50 cm from the eye and illuminate it with a desk lamp. Find the image on the retina.
Move your hand until the image is sharp.
Describe the image: Is it inverted or upright? What is the approximate magnification?
If the image is inverted, why does the world not look upside down to us?
(b) Replace the plastic lens with the adjustable water filled lens. Use the optics light box
as an object and place it about 20 cm from the eye.
(c) With the plunger, GENTLY adjust the shape of the lens until the image is relatively
focused (it won’t get perfect).
(d) Now move the light source farther from the eye until the image gets fuzzy. Before
trying it, make a prediction:
How you will need to adjust the lens to focus the image now – more converging or
less converging? Why?
Try it, see if you were right, and report on your results.
(e) Insert the black plastic ‘pupil’ into slot A. This simulates squinting or a closed-up
pupil in bright light. How does this affect the image?
Part 4B: The Human Eye – Nearsightedness and Farsightedness
For this station, we’ll use a fixed lens marked 62 inside the eye to represent the eye’s
lens. Keep this lens in place the whole time.
(a) With the retina (white plastic screen) in the “normal” position, find the near point of
this eye (that is, the closest distance it can see clearly). What is this distance?
(b) Farsighted Eye: A farsighted person has a shorter than normal eyeball, making the
screen too close to the lens. Simulate this by moving the white retina screen closer to
the lens, to the position labeled “FAR.”
(c) Describe what happens to the image. This is what a far sighted person sees when
trying to look at a near object. Now have the eye model ‘look’ at the far away light
source. Is it clearer? Why?
(e) Make the eye look back at the near object. If you were designing glasses to help this
eye see the near object, would you use converging or diverging lenses? Why? Find a
lens in the set that makes a clearer image (remember, + focal lengths are converging
and – ones are diverging). Which one did you use?
(f) Near sighted eye. A nearsighted person has a longer than normal eyeball, making the
screen (retina) too far from the lens. Simulate this by moving the white retina screen
farther from the lens, to the position labeled “NEAR.”
Describe the images produced by both near and far objects. Which one is clearer?
(g) What kind of glasses would help this eye see the far object - converging or diverging
lenses? Why? Find a lens in the set that makes a clear image. Which one did you use?
Part 5: Two-Lens System
(a) Mount a light source near one end of the optical bench and place a converging lens
with focal length f = 10 cm (100 mm) at a distance of 30 cm from the light source.
(b) Place a diverging lens of focal length f = –15 cm (-150 mm) at a distance of 10 cm
from the first lens.
(c) Using the thin-lens and magnification equations, predict the images distance ( ithy ) and
the magnification of the image mthy for this two-lens system.
(d) Use a screen to find the image location iexpt and the magnification mexpt. Compare ithy
and iexpt using a percent difference. How do they compare?
Part 6A: Lens-Mirror System
(a) Mount a light source near one end of the optical bench and place a converging lens
with focal length f = 10 cm (100 mm) at a distance of 20 cm from the light source.
(b) Place a concave mirror of focal length f = 5 cm at a distance of 35 cm from the first
lens.
(c) Using the thin-lens and mirror equations, predict the images distance ( ithy ) for this
lens-mirror system.
(d) Use a half-screen to find the image location iexpt . Compare ithy and iexpt using a
percent difference. How do they compare?
Part 6B:Telescope
(a) Look at the model telescope that is set up.
What kind of lens (converging or diverging) and mirror (concave or convex) does it
use.
Describe how the telescope works. What is the function of the mirror? What is the
function of the lens?